Speaking of large but finite numbers, I think sometimes we forget just how big some finite numbers can be:
This article really stretched my brain/hurt my head: https://waitbutwhy.com/2014/11/1000000-grahams-number.html Numbers can be so big they become scary. Jason On Sat, May 23, 2020 at 6:37 PM Russell Standish <[email protected]> wrote: > On Sat, May 23, 2020 at 12:05:08PM -0700, 'Brent Meeker' via Everything > List wrote: > > > > > > On 5/23/2020 4:42 AM, Bruno Marchal wrote: > > > > > > Well, those are theorem provable in very weak theories. It is more a > > > question of grasping the proof than subscribing to a philosophical > idea. > > > That arithmetic executes all programs is a theorem similar to Euclid’s > > > theorem that there is no biggest prima numbers. It is more a fact, than > > > an idea which could be debated. I insist on this as I realise this is > > > less known by the general scientists than 20 years ago. We knew this > > > implicitly since Gödel 1931, and explicitly since Church, Turing and > > > Kleene 1936. > > > > Recently you have said that your theory is consistent with finitism, even > > ultrafinitism. But the idea that arithemtic exectues all programs > certainly > > requires infinities. > > Only potential infinities, not actual infinities. For the UD (a finite > object) to execute any given program, one only needs to wait a finite > amount of time. > > However, I would think that ultrafinitism would change COMP's > predictions, and in a sense be incompatibe with it. Some programs will > not exist, because one would need to wait too long for them to be > executed by the UD. In fact, the choice of reference universal machine > would be significant in ultrafinitism, IIUC. > > > -- > > > ---------------------------------------------------------------------------- > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders [email protected] > http://www.hpcoders.com.au > > ---------------------------------------------------------------------------- > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/20200523233705.GC27696%40zen > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUgRf%2BTqhT-nXF8s5vGFQo%2BHrD55fFObFLESRKDL32PSyQ%40mail.gmail.com.
